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Byju's Answer
Standard IX
Mathematics
Volume of a right circular cone
The radius an...
Question
The radius and slant height of a cone are in the ratio 1:3. The volume of cone is 452.16 root 2 cm
3
. Find the height of the cone. (Take pie = 3.14)
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Solution
Let
the
radius
of
base
of
cone
=
r
Let
the
height
of
cone
=
h
Let
the
slant
height
of
cone
=
l
Now
,
r
l
=
1
3
⇒
l
=
3
r
.
.
.
.
.
1
Now
,
h
2
=
l
2
-
r
2
=
3
r
2
-
r
2
=
9
r
2
-
r
2
=
8
r
2
⇒
h
=
2
2
r
Now
,
volume
of
cone
=
452
.
16
2
cm
3
⇒
1
3
πr
2
h
=
452
.
16
2
⇒
1
3
×
3
.
14
×
r
2
×
2
2
r
=
452
.
16
2
⇒
r
3
=
452
.
16
2
×
3
3
.
14
×
2
⇒
r
3
=
216
⇒
r
=
6
cm
Now
,
height
,
h
=
2
2
r
=
2
2
×
6
=
12
2
cm
=
12
×
1
.
414
=
16
.
968
cm
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